Final answer:
The perpendicular bisector of the line segment EF with end points E(-1,-3) and F(5,5) has a slope of -3/4 and passes through the midpoint (2,1). The equation is 3x + 4y = 10 after simplifying. Therefore, none of the provided options A-D is correct.
Step-by-step explanation:
To find the perpendicular bisector of the line segment EF with end points E(-1,-3) and F(5,5), we need to find the midpoint of EF and the slope of the line perpendicular to EF.
First, we calculate the midpoint M of EF using the midpoint formula, M = \((\frac{x1 + x2}{2}, \frac{y1 + y2}{2})\), which gives us M = (2, 1).
Next, we calculate the slope of EF. The slope of a line passing through points \((x1, y1)\) and \((x2, y2)\) is given by the formula \(m = \frac{y2 - y1}{x2 - x1}\). For points E and F, the slope is \(m = \frac{5 - (-3)}{5 - (-1)} = \frac{8}{6} = \frac{4}{3}\).
The slope of the perpendicular bisector is the negative reciprocal of the slope of EF, which is \(-\frac{3}{4}\). Using the point-slope form of a line, \(y - y1 = m(x - x1)\), where \(m\) is the slope and \((x1, y1)\) is a point on the line (in this case, the midpoint M), we write the equation of the bisector: \(y - 1 = -\frac{3}{4}(x - 2)\).
Finally, simplifying the equation yields \(4y - 4 = -3x + 6\), or \(3x + 4y = 10\), which isn't one of the provided options A-D. Thus, none of the options given is the correct perpendicular bisector of line segment EF.